Geodesic
Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 567-573

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Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.
Keywords: edge-connectivity, clique number, maximally edge-connected graphs, super-edge-connected graphs 
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     author = {Volkmann, Lutz},
     title = {Sufficient {Conditions} for {Maximally} {Edge-Connected} and {Super-Edge-Connected} {Graphs} {Depending} on {The} {Clique} {Number}},
     journal = {Discussiones Mathematicae. Graph Theory},
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Volkmann, Lutz. Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 567-573. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a18/